Geodesic
An efficient estimator for Gibbs random fields
Kybernetika, Tome 50 (2014) no. 6, pp. 883-895

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An efficient estimator for the expectation $\int f \d P$ is constructed, where $P$ is a Gibbs random field, and $f$ is a local statistic, i. e. a functional depending on a finite number of coordinates. The estimator coincides with the empirical estimator under the conditions stated in Greenwood and Wefelmeyer [6], and covers the known special cases, namely the von Mises statistic for the i.i.d. underlying fields and the case of one-dimensional Markov chains.
DOI : 10.14736/kyb-2014-6-0883
Classification : 62F12, 62M40
Keywords: Gibbs random field; efficient estimator; empirical estimator 
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     author = {Jan\v{z}ura, Martin},
     title = {An efficient estimator for {Gibbs} random fields},
     journal = {Kybernetika},
     pages = {883--895},
     publisher = {mathdoc},
     volume = {50},
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     year = {2014},
     doi = {10.14736/kyb-2014-6-0883},
     mrnumber = {3301777},
     zbl = {06416865},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2014-6-0883/}
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Janžura, Martin. An efficient estimator for Gibbs random fields. Kybernetika, Tome 50 (2014) no. 6, pp. 883-895. doi: 10.14736/kyb-2014-6-0883

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